Control of Nonlinear Systems with Reach-Avoid-Stay Specifications: A Lyapunov-Barrier Approach with an Application to the Moore-Greizer Model
Bibliographic record
Abstract
The study of control synthesis for reach-avoid-stay objectives for nonlinear systems has received considerable interest in recent years. Such objectives can be naturally treated as a formal specification and effectively handled by formal methods. While formal methods often rely on constructing a finite-state approximation and developing algorithms to capture the winning set (a set of initial states from which a controller exists to realize the given task), Lyapunov methods can characterize stability and safety properties without having to discretize the state space. Inspired by recent work on converse Lyapunov-barrier theorems, we propose control Lyapunov-barrier functions to provide sufficient conditions for control synthesis with reach-avoid-stay specifications. A comparison between the proposed Lyapunov method and formal methods based on a fixed-point algorithm is illustrated by an application to enhancing the performance of jet engine compressors, which is based on a reduced Moore-Greitzer nonlinear ODE model. We apply a quadratic programming (QP) framework to reactively synthesize controllers in the case study.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".